Sure, let's solve each part step-by-step:
### Part (i)
[tex]\[
\frac{2}{3} \times 5_5^{1 \frac{1}{5}}
\][/tex]
The given fraction [tex]\(5_5^{1 \frac{1}{5}}\)[/tex] is quite ambiguous. If we assume it's equivalent to 1 (since the fraction provided in the Python code assumed [tex]\(\frac{1}{1}\)[/tex]), we get:
[tex]\[
\frac{2}{3} \times 1 = \frac{2}{3}
\][/tex]
So the result is:
[tex]\[
\frac{2}{3}
\][/tex]
### Part (ii)
[tex]\[
\frac{2}{7} \times \frac{1}{3}
\][/tex]
Let's multiply the numerators together and the denominators together:
[tex]\[
\frac{2 \times 1}{7 \times 3} = \frac{2}{21}
\][/tex]
So the result is:
[tex]\[
\frac{2}{21}
\][/tex]
### Part (iii)
[tex]\[
\frac{9}{3} \times \frac{5}{5}
\][/tex]
First, simplify each fraction:
[tex]\[
\frac{9}{3} = 3 \quad \text{and} \quad \frac{5}{5} = 1
\][/tex]
Now, multiply the simplified fractions:
[tex]\[
3 \times 1 = 3
\][/tex]
So the result is:
[tex]\[
3
\][/tex]
### Part (iv)
[tex]\[
\frac{9}{5} \times \frac{10}{4} \times \frac{1}{2}
\][/tex]
First, let's multiply the fractions together:
[tex]\[
\frac{9 \times 10 \times 1}{5 \times 4 \times 2} = \frac{90}{40}
\][/tex]
Next, simplify [tex]\( \frac{90}{40} \)[/tex] by dividing both the numerator and denominator by their greatest common divisor, which is 10:
[tex]\[
\frac{90 \div 10}{40 \div 10} = \frac{9}{4}
\][/tex]
So the result is:
[tex]\[
\frac{9}{4}
\][/tex]
### Final Results
Each part yields the following results:
1. [tex]\( \frac{2}{3} \)[/tex]
2. [tex]\( \frac{2}{21} \)[/tex]
3. [tex]\( 3 \)[/tex]
4. [tex]\( \frac{9}{4} \)[/tex]
So, putting it all together:
[tex]\[
\left[ \frac{2}{3}, \frac{2}{21}, 3, \frac{9}{4} \right]
\][/tex]
